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Physical Review Letters

Ising Model with a Transverse Field

Roger James Elliott, Pierre M. Pfeuty, C Wood

Published Aug 17, 1970• 143 citations
Publisher

Abstract

The phase transition in the Ising model has been studied as a function of an applied transverse field, by Green's function and series-expansion methods. The critical indices are probably independent of the applied field except at $T=0$ where they appear to be related to those of the Ising model in one higher dimension.

DOI
10.1103/physrevlett.25.443

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International Journal of Modern Physics B•Oct 20, 2002•5 citations
The phase transition in the Ising model has been studied as a function of an applied transverse field, by Green's function and series-expansion methods. The critical indices are probably independent of the applied field except at T=0T=0T=0 where they appear to be related to those of the Ising model in one higher dimension.
For Pt. I see ibid., vol. 4, 2359 (1971). The properties of the Ising model with a transverse field, with the Hamiltonian written H=- Gamma Sigma i S i x - 1 / 2 Sigma i,j J ij S i z S j z , are studied by perturbation expansions at T=0 in the ground state, both below and above the critical field Gamma C , for an hypercubic lattice and short range interactions. The order parameter (S z ) and the correlation function G=) Sigma i S i z Sigma j S j z ) are calculated respectively below and above Gamma C . The gap in the excitation spectrum is also studied above the critical field. The critical behaviour obtained from these expansions at T=0 is different from that obtained at T finite and is shown to be analogous to the critical behaviour of the Ising model for a lattice with one more dimension.